/usr/include/viennacl/linalg/cg.hpp is in libviennacl-dev 1.5.2-2.
This file is owned by root:root, with mode 0o644.
The actual contents of the file can be viewed below.
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100 101 102 103 104 105 106 107 108 109 110 111 112 113 114 115 116 117 118 119 120 121 122 123 124 125 126 127 128 129 130 131 132 133 134 135 136 137 138 139 140 141 142 143 144 145 146 147 148 149 150 151 152 153 154 155 156 157 158 159 160 161 162 163 164 165 166 167 168 169 170 171 172 173 174 175 176 177 178 179 180 181 182 183 184 185 186 187 188 189 190 191 192 193 194 195 196 197 198 199 200 201 202 203 204 205 206 207 208 209 210 211 212 213 | #ifndef VIENNACL_LINALG_CG_HPP_
#define VIENNACL_LINALG_CG_HPP_
/* =========================================================================
Copyright (c) 2010-2014, Institute for Microelectronics,
Institute for Analysis and Scientific Computing,
TU Wien.
Portions of this software are copyright by UChicago Argonne, LLC.
-----------------
ViennaCL - The Vienna Computing Library
-----------------
Project Head: Karl Rupp rupp@iue.tuwien.ac.at
(A list of authors and contributors can be found in the PDF manual)
License: MIT (X11), see file LICENSE in the base directory
============================================================================= */
/** @file viennacl/linalg/cg.hpp
@brief The conjugate gradient method is implemented here
*/
#include <vector>
#include <map>
#include <cmath>
#include "viennacl/forwards.h"
#include "viennacl/tools/tools.hpp"
#include "viennacl/linalg/ilu.hpp"
#include "viennacl/linalg/prod.hpp"
#include "viennacl/linalg/inner_prod.hpp"
#include "viennacl/linalg/norm_2.hpp"
#include "viennacl/traits/clear.hpp"
#include "viennacl/traits/size.hpp"
#include "viennacl/meta/result_of.hpp"
namespace viennacl
{
namespace linalg
{
/** @brief A tag for the conjugate gradient Used for supplying solver parameters and for dispatching the solve() function
*/
class cg_tag
{
public:
/** @brief The constructor
*
* @param tol Relative tolerance for the residual (solver quits if ||r|| < tol * ||r_initial||)
* @param max_iterations The maximum number of iterations
*/
cg_tag(double tol = 1e-8, unsigned int max_iterations = 300) : tol_(tol), iterations_(max_iterations) {}
/** @brief Returns the relative tolerance */
double tolerance() const { return tol_; }
/** @brief Returns the maximum number of iterations */
unsigned int max_iterations() const { return iterations_; }
/** @brief Return the number of solver iterations: */
unsigned int iters() const { return iters_taken_; }
void iters(unsigned int i) const { iters_taken_ = i; }
/** @brief Returns the estimated relative error at the end of the solver run */
double error() const { return last_error_; }
/** @brief Sets the estimated relative error at the end of the solver run */
void error(double e) const { last_error_ = e; }
private:
double tol_;
unsigned int iterations_;
//return values from solver
mutable unsigned int iters_taken_;
mutable double last_error_;
};
/** @brief Implementation of the conjugate gradient solver without preconditioner
*
* Following the algorithm in the book by Y. Saad "Iterative Methods for sparse linear systems"
*
* @param matrix The system matrix
* @param rhs The load vector
* @param tag Solver configuration tag
* @return The result vector
*/
template <typename MatrixType, typename VectorType>
VectorType solve(const MatrixType & matrix, VectorType const & rhs, cg_tag const & tag)
{
//typedef typename VectorType::value_type ScalarType;
typedef typename viennacl::result_of::value_type<VectorType>::type ScalarType;
typedef typename viennacl::result_of::cpu_value_type<ScalarType>::type CPU_ScalarType;
//std::cout << "Starting CG" << std::endl;
VectorType result = rhs;
viennacl::traits::clear(result);
VectorType residual = rhs;
VectorType p = rhs;
VectorType tmp = rhs;
CPU_ScalarType ip_rr = viennacl::linalg::inner_prod(rhs,rhs);
CPU_ScalarType alpha;
CPU_ScalarType new_ip_rr = 0;
CPU_ScalarType beta;
CPU_ScalarType norm_rhs = std::sqrt(ip_rr);
//std::cout << "Starting CG solver iterations... " << std::endl;
if (norm_rhs == 0) //solution is zero if RHS norm is zero
return result;
for (unsigned int i = 0; i < tag.max_iterations(); ++i)
{
tag.iters(i+1);
tmp = viennacl::linalg::prod(matrix, p);
alpha = ip_rr / viennacl::linalg::inner_prod(tmp, p);
result += alpha * p;
residual -= alpha * tmp;
new_ip_rr = viennacl::linalg::norm_2(residual);
if (new_ip_rr / norm_rhs < tag.tolerance())
break;
new_ip_rr *= new_ip_rr;
beta = new_ip_rr / ip_rr;
ip_rr = new_ip_rr;
p = residual + beta * p;
}
//store last error estimate:
tag.error(std::sqrt(new_ip_rr) / norm_rhs);
return result;
}
template <typename MatrixType, typename VectorType>
VectorType solve(const MatrixType & matrix, VectorType const & rhs, cg_tag const & tag, viennacl::linalg::no_precond)
{
return solve(matrix, rhs, tag);
}
/** @brief Implementation of the preconditioned conjugate gradient solver
*
* Following Algorithm 9.1 in "Iterative Methods for Sparse Linear Systems" by Y. Saad
*
* @param matrix The system matrix
* @param rhs The load vector
* @param tag Solver configuration tag
* @param precond A preconditioner. Precondition operation is done via member function apply()
* @return The result vector
*/
template <typename MatrixType, typename VectorType, typename PreconditionerType>
VectorType solve(const MatrixType & matrix, VectorType const & rhs, cg_tag const & tag, PreconditionerType const & precond)
{
typedef typename viennacl::result_of::value_type<VectorType>::type ScalarType;
typedef typename viennacl::result_of::cpu_value_type<ScalarType>::type CPU_ScalarType;
VectorType result = rhs;
viennacl::traits::clear(result);
VectorType residual = rhs;
VectorType tmp = rhs;
VectorType z = rhs;
precond.apply(z);
VectorType p = z;
CPU_ScalarType ip_rr = viennacl::linalg::inner_prod(residual, z);
CPU_ScalarType alpha;
CPU_ScalarType new_ip_rr = 0;
CPU_ScalarType beta;
CPU_ScalarType norm_rhs_squared = ip_rr;
CPU_ScalarType new_ipp_rr_over_norm_rhs;
if (norm_rhs_squared == 0) //solution is zero if RHS norm is zero
return result;
for (unsigned int i = 0; i < tag.max_iterations(); ++i)
{
tag.iters(i+1);
tmp = viennacl::linalg::prod(matrix, p);
alpha = ip_rr / viennacl::linalg::inner_prod(tmp, p);
result += alpha * p;
residual -= alpha * tmp;
z = residual;
precond.apply(z);
new_ip_rr = viennacl::linalg::inner_prod(residual, z);
new_ipp_rr_over_norm_rhs = new_ip_rr / norm_rhs_squared;
if (std::fabs(new_ipp_rr_over_norm_rhs) < tag.tolerance() * tag.tolerance()) //squared norms involved here
break;
beta = new_ip_rr / ip_rr;
ip_rr = new_ip_rr;
p = z + beta*p;
}
//store last error estimate:
tag.error(std::sqrt(std::fabs(new_ip_rr / norm_rhs_squared)));
return result;
}
}
}
#endif
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